Lung lamellar body amphiphilic topography: A morphological evaluation using the continuum theory of liquid crystals: I. Closed surfaces: Closed spheres, Concentric tori, and Dupin cyclides

1988 ◽  
Vol 221 (1) ◽  
pp. 503-519 ◽  
Author(s):  
C. J. Stratton ◽  
J. A. N. Zasadzinski ◽  
D. Elkins
Keyword(s):  
Liquid Crystals ◽  
Lamellar Body ◽  
Continuum Theory ◽  
Closed Surfaces ◽  
Morphological Evaluation ◽  
Dupin Cyclides ◽  
The Continuum

Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

1983 ◽  
Vol 41 ◽  
pp. 646-647
Author(s):  
Joseph A. Zasadzinski
Keyword(s):  
Liquid Crystalline ◽  
Freeze Fracture ◽  
Continuum Theory ◽  
Closed Surfaces ◽  
Straight Line ◽  
Low Weight ◽  
Concentric Spheres ◽  
Membrane Geometry ◽  
Dupin Cyclides ◽  
Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

A continuum theory of disorder in nematic liquid crystals. - II. Intermolecular correlations

1977 ◽  
Vol 353 (1673) ◽  
pp. 261-275 ◽  
Keyword(s):  
Liquid Crystals ◽  
Order Parameter ◽  
Continuum Theory ◽  
The Other ◽  
Wave Number ◽  
Interesting Problem ◽  
Molecular Models ◽  
Partial Agreement ◽  
The Mean ◽  
The Continuum

The continuum theory of nematics suggested in paper I is used to derive an expression for the quantity < P 2 (cos γ ( R ))>, where γ is the angle between the director at two points separated by a distance R . The result tends to the Maier-Saupe limit (S 2 2 , corresponding to no correlations of orientation) for large R , but to unity for small R , while for the value of R corresponding to the mean intermolecular spacing it is about S α 0 2 , with α 0 close to unity. It is suggested that continuum theory may be used to estimate <sin γ ( R )> as well. Two simple molecular models for nematics are discussed in the light of these results, one of them a simplified version of the model on which Maier & Saupe originally based their theory, and the other a steric model of the sort proposed by Onsager. Predictions based upon these models concerning the Frank stiffness constants - in particular, concerning their dependence on the order parameter S 2 at constant volume and temperature and upon wave number q - are found to be in partial but only partial agreement with experiment. An interesting problem concerning the entropy of misalignment and its effect upon the stiffness of a nematic is left unresolved.

The effect of the elastic constants on the alignment and electro-optic behaviour of smectic C liquid crystals

1997 ◽  
Vol 8 (3) ◽  
pp. 281-291 ◽  
Author(s):  
C. V. BROWN ◽  
P. E. DUNN ◽  
J. C. JONES
Keyword(s):  
Liquid Crystals ◽  
Elastic Constants ◽  
Tilt Angle ◽  
Applied Electric Field ◽  
Continuum Theory ◽  
Optical Studies ◽  
Smectic C ◽  
Electro Optic ◽  
Surface Comparison ◽  
The Continuum

The static electro-optic behaviour of achiral smectic C samples in the chevron geometry have been modelled using the continuum theory of Leslie et al. [1]. The model assumes that the layer tilt and smectic C director tilt angle are constant, and treats the layers at the chevron interface as an infinitely bound surface. Comparison of the predicted electro-optic behaviour with experimental results gives values for the bend (B1) and splay (B2) c-director elastic constants. However, more detailed optical studies show that surface and chevron interface terms become important at high values of applied electric field.

Confirming the continuum theory of dynamic brittle fracture for fast cracks

Nature ◽  
10.1038/16891 ◽  
1999 ◽  
Vol 397 (6717) ◽  
pp. 333-335 ◽  
Author(s):  
Eran Sharon ◽  
Jay Fineberg
Keyword(s):  
Brittle Fracture ◽  
Continuum Theory ◽  
Dynamic Brittle Fracture ◽  
The Continuum

scholarly journals Matrix integrals & finite holography

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Dionysios Anninos ◽  
Beatrix Mühlmann
Keyword(s):  
Critical Exponents ◽  
Continuum Theory ◽  
Point Of View ◽  
Leading Order ◽  
Minimal Models ◽  
Point Evaluation ◽  
Brst Cohomology ◽  
Matrix Integrals ◽  
The Matrix ◽  
The Continuum

Abstract We explore the conjectured duality between a class of large N matrix integrals, known as multicritical matrix integrals (MMI), and the series (2m − 1, 2) of non-unitary minimal models on a fluctuating background. We match the critical exponents of the leading order planar expansion of MMI, to those of the continuum theory on an S2 topology. From the MMI perspective this is done both through a multi-vertex diagrammatic expansion, thereby revealing novel combinatorial expressions, as well as through a systematic saddle point evaluation of the matrix integral as a function of its parameters. From the continuum point of view the corresponding critical exponents are obtained upon computing the partition function in the presence of a given conformal primary. Further to this, we elaborate on a Hilbert space of the continuum theory, and the putative finiteness thereof, on both an S2 and a T2 topology using BRST cohomology considerations. Matrix integrals support this finiteness.

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